Question 1065302
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Nine Years ago, Frank was half as old as Marilyn. Now his age is two thirds her age. Find their ages now. WITH WORK PLEASE
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<pre>
Let F be the Frank's present age, M be the Marilyn's present age.

9 years ago Frank was (F-9) years old, while Marilyn was (M-9) years old.

The condition says 

F - 9 = {{{(1/2)*(M-9)}}}.   (1)     ("Nine Years ago, Frank was half as old as Marilyn")

Now his age is two thirds her age:

F = {{{(2/3)*M}}}.           (2)

Substitute (2) into equation (1) replacing F. You will get

{{{(2/3)*M-9}}} = {{{(1/2)*(M-9)}}}.

You have a single equation for single unknown M. To solve it, multiply both sides by 6 to rid of denominators. You will get

4M - 54 = 3*(M-9),

4M - 54 = 3M - 27,

4M - 3M = -27 + 54,

M = 27.

So, we found Marilyn present age is 27 years.

Then from (2) Franklin 18 = {{{(2/3)*27}}} years old.
</pre>

Solved.


There is a bunch of lessons on age word problems 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Age-problems-and-their-solutions.lesson>Age problems and their solutions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Fresh-formulation-of-a-traditional-age-problem.lesson>A fresh formulation of a traditional age problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Really-intricate-age-word-problem.lesson>Really intricate age word problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Selected-age-word-problems-from-the-archive.lesson>Selected age word problems from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problem-for-the-day-of-April-1.lesson>Age problem for the day of April, 1</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/04-OVERVIEW-of-lessons-on-age-problems.lesson>OVERVIEW of lessons on age problems</A>

in this site.


Read them and become an expert in solving age problems.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Age word problems</U>".